Evolution of Geometric Sensitivity Derivatives from Computer Aided Design Models

The generation of design parameter sensitivity derivatives is required for gradient-based optimization. Such sensitivity derivatives are elusive at best when working with geometry defined within the solid modeling context of Computer-Aided Design (CAD) systems. Solid modeling CAD systems are often proprietary and always complex, thereby necessitating ad hoc procedures to infer parameter sensitivity. A new perspective is presented that makes direct use of the hierarchical associativity of CAD features to trace their evolution and thereby track design parameter sensitivity. In contrast to ad hoc methods, this method provides a more concise procedure following the model design intent and determining the sensitivity of CAD geometry directly to its respective defining parameters

Fast parametric analysis of trimmed multi-patch isogeometric Kirchhoff-Love shells using a local reduced basis method

This contribution presents a model order reduction framework for real-time efficient solution of trimmed, multi-patch isogeometric Kirchhoff-Love shells. In several scenarios, such as design and shape optimization, multiple simulations need to be performed for a given set of physical or geometrical parameters. This step can be computationally expensive in particular for real world, practical applications. We are interested in geometrical parameters and take advantage of the flexibility of splines in representing complex geometries. In this case, the operators are geometry-dependent and generally depend on the parameters in a non-affine way. Moreover, the solutions obtained from trimmed domains may vary highly with respect to different values of the parameters. Therefore, we employ a local reduced basis method based on clustering techniques and the Discrete Empirical Interpolation Method to construct affine approximations and efficient reduced order models. In addition, we discuss the application of the reduction strategy to parametric shape optimization. Finally, we demonstrate the performance of the proposed framework to parameterized Kirchhoff-Love shells through benchmark tests on trimmed, multi-patch meshes including a complex geometry. The proposed approach is accurate and achieves a significant reduction of the online computational cost in comparison to the standard reduced basis method.Comment: 43 pages, 21 figures, 3 table

Shape optimization directly from CAD: an isogeometric boundary element approach

The present thesis addresses shape sensitivity analysis and optimization in linear elasticity with the isogeometric boundary element method (IGABEM), where the basis functions used for constructing geometric models in computer-aided design (CAD) are also employed to discretize the boundary integral equation (BIE) for structural analysis, and to discretize the material differentiation form of the BIE for shape sensitivity analysis. To guarantee water-tight and locally-refined geometries, we use non-uniform rational B-splines (NURBS) and T-splines for two-dimensional and three dimensional problems, respectively. In addition, we take advantage of the regularized form of BIE instead of the singular form, to bypass the difficulties caused by the evaluation of strongly singular integrals and jump terms. The main advantages of the present work arise from the ability of the IGABEM to seamlessly integrate CAD and numerical analysis, since they share the same boundary representation of geometric models. Therefore, throughout the whole shape optimization, it does not need a costly meshing/remeshing procedure. Moreover, the control points can be naturally chosen as the design variables, and the optimal solution can be directly returned to the CAD system without any smoothing procedure